Co-sparse Non-negative Matrix Factorization

Non-negative matrix factorization, which decomposes the input non-negative matrix into product of two non-negative matrices, has been widely used in the neuroimaging field due to its flexible interpretability with non-negativity property. Nowadays, especially in the neuroimaging field, it is common to have at least thousands of voxels while the sample size is only hundreds. The non-negative matrix factorization encounters both computational and theoretical challenge with such high-dimensional data, i.e., there is no guarantee for a sparse and part-based representation of data. To this end, we introduce a co-sparse non-negative matrix factorization method to high-dimensional data by simultaneously imposing sparsity in both two decomposed matrices. Instead of adding some sparsity induced penalty such as l1 norm, the proposed method directly controls the number of non-zero elements, which can avoid the bias issues and thus yield more accurate results. We developed an alternative primal-dual active set algorithm to derive the co-sparse estimator in a computationally efficient way. The simulation studies showed that our method achieved better performance than the state-of-art methods in detecting the basis matrix and recovering signals, especially under the high-dimensional scenario. In empirical experiments with two neuroimaging data, the proposed method successfully detected difference between Alzheimer's patients and normal person in several brain regions, which suggests that our method may be a valuable toolbox for neuroimaging studies.

Pemodelan Vektor Metode Interior Point Untuk Studi Pembebanan Maksimum Sistem Tenaga Listrik

Beberapa tahun terakhir, pada sistem tenaga listrik beban yang ada semakin besar seiring peningkatan beban listrik. Permasalahan utama kondisi pembebanan akan menyebabkan ketidakstabilan tegangan di sistem tenaga listrik. Untuk mencegah ketidakstabilan sistem, penting bagi operator sistem tenaga untuk mengidentifikasi seberapa jauh sistem memuat dari kondisi kritisnya. Penelitian ini membahas masalah maksimum pembebanan dengan menggunakan metode non-linear primal-dual interior point method. Caranya dengan memaksimalkan beban sistem yang diwakili oleh pengganda skalar ke beban sistem. Kontribusi utama dari pekerjaan ini adalah dalam pengembangan model vectorized dari masalah dan pengembangan program aplikasi dalam bahasa pemrograman Pyhton. Model yang dikembangkan kemudian diuji untuk memecahkan masalah loadability maksimum untuk sistem pengujian IEEE 14-bus dan 30-bus. Simulasi dari model ini dan program komputer yang dikembangkan memberikan hasil yang memuaskan.Kata Kunci : Python, Interior Point Method. Loadability Maksimum, dan Model Vectorized

On a primal-dual Newton proximal method for convex quadratic programs

This paper introduces QPDO, a primal-dual method for convex quadratic programs which builds upon and weaves together the proximal point algorithm and a damped semismooth Newton method. The outer proximal regularization yields a numerically stable method, and we interpret the proximal operator as the unconstrained minimization of the primal-dual proximal augmented Lagrangian function. This allows the inner Newton scheme to exploit sparse symmetric linear solvers and multi-rank factorization updates. Moreover, the linear systems are always solvable independently from the problem data and exact linesearch can be performed. The proposed method can handle degenerate problems, provides a mechanism for infeasibility detection, and can exploit warm starting, while requiring only convexity. We present details of our open-source C implementation and report on numerical results against state-of-the-art solvers. QPDO proves to be a simple, robust, and efficient numerical method for convex quadratic programming.

SPITFIR(e): A supermaneuverable algorithm for restoring 2D-3D fluorescence images and videos, and background subtraction

While fluorescent microscopy imaging has become the spearhead of modern biology as it is able to generate long-term videos depicting 4D nanoscale cell behaviors, it is still limited by the optical aberrations and the photon budget available in the specimen and to some extend to photo-toxicity. A direct consequence is the necessity to develop flexible and "off-road" algorithms in order to recover structural details and improve spatial resolution, which is critical when pushing the illumination to the low levels in order to limit photo-damages. Moreover, as the processing of very large temporal series of images considerably slows down the analysis, special attention must be paid to the feasibility and scalability of the developed restoration algorithms. To address these specifications, we present a very flexible method designed to restore 2D-3D+Time fluorescent images and subtract undesirable out-of-focus background. We assume that the images are sparse and piece-wise smooth, and are corrupted by mixed Poisson-Gaussian noise. To recover the unknown image, we consider a novel convex and non-quadratic regularizer Sparse Hessian Variation) defined as the mixed norms which gathers image intensity and spatial second-order derivatives. This resulting restoration algorithm named SPITFIR(e) (SParse fIT for Fluorescence Image Restoration) utilizes the primal-dual optimization principle for energy minimization and can be used to process large images acquired with varied fluorescence microscopy modalities. It is nearly parameter-free as the practitioner needs only to specify the amount of desired sparsity (weak, moderate, high). Experimental results in lattice light sheet, stimulated emission depletion, multifocus microscopy, spinning disk confocal, and wide-field microscopy demonstrate the generic ability of the SPITFIR(e) algorithm to efficiently reduce noise and blur, and to subtract undesirable fluorescent background, while avoiding the emergence of deconvolution artifacts.